Spherometer



W H. H. WILLIS i"*-.?

SPHEROMETER Filed Dec. 29, 1931 3 Sheets-Sheet l INVENTOR amw M 2%. M v

' liNEW SPHEROMETER Filed Dec. 29, 1931 3 Sheets-Sheet 2 INVEN 447mgM/Ms.

( TORNEY.

bility of such instruments by employing a less Patented Aug. 2 5, 19 36ma ns PATENT etect Horace H. Willis, Pelham. N e Y assignor to ""Sprry"Gyroscope" Company, Ina, Brooklyn,- N;-Y;.-, a corporation-of New orkwee eateni 3 seria No- 5.

14 Claims. (01. ea -A52) the centralball. In addition it secure be notedthat this type ofinstrurneritineasiiresthe r us of asphere'determiriedby th'fourpoints of con: tact of the balls andtne worksurtace.

Accordingto my invention I propose to greatly simplify and at the sametime increa s'etpe'fle i number" of balls; preferably three arrangediri'a rhw'ian'd touching." Means are provided'to con strain the motionof the balls so thatwhatever their possible position, the planedetermined'by their centers remains fixed with respectto'the instrument.Also, to permitthe' raising and lowering of the middle ball and atthe sA keep the balls touching; I provide a means for permitting lateralmotion; i. e, 'variatioh in the distance betweenthe centers of theballs. By employing touching balls, the usual complicated formu o d rthe eams of C r at r Q a spherical or other curved si ence is"greatlysimplified and may be determinedby either the vertical displacement ofthe center or middle ball the line joining their centers;

Another object of the invention is to improve and simplify this type of'spherometer so that great accuracy is secured without complication. Bymy invention I provide 'aninstrument which measures the radius of acircle determined by the three points of contactbetwenthe .balls and thework surface. In the event it is desired to measure the radius of aspherical surface with the in rum n t n cessa n su ficien cr terion thatthe radius of the measured circle equal the radius of the sphere is thatthe three points of contactlie in the plane determined by the cenene theballs. Iriothr words, means are provided whereby radii oigreat-circlescan be measured. It "tobe noted} that this provides an accurate methodfor' determining departures from sphericity of a givenunknow'n surface.In

addition the invention provides a means for In ring the curvature aswellas the space rate oi change of curvature of any-surface to aprecision limited only by the conditions oi the probleminhand;"Ifhusmydevice may he used to measure 'the"curvature ofanyinathematically surface by measuring the same at a Illll'l'lher of'pointsto obtain the space rate of *change of curvature from which thecharacter or equation the'curve mayhe obtained. Therefore;myinvention'poss'e'sses a distinct advantage over prior typesoi'spherome'ters which are useless except on surfaces havi' uniformradii of curvahc antp Hi 5.1 1 Referring to the drawings showing severalpre ferred'forins or the invention} hi 1 is h t?? e ev tes of m ph eFig. 2 i'sfa verticalsection taken-0n line 2--2 of .w l 1 g .L Y

3 is a rear elevation of the center portion only or the registeringmechanism;

Fig: 4' is" aner'r larged viewer the mounting for th" 'entralballi FigfiEiis' a" front elevation with parts broken away of the holder iorone ofthe end balls. "r'igflc fisa' similaryiew of the holder for the otherend halljwhich inthis caseis the adjustbi b u Figf'? is a diagramillustrating the use of the device in obtaining the radiushi curvatureof a wh n? s iiia Fig. 8 is a similar view showing how the device isused on a sphere or convex surface.

Fig. 9 is a iront elevation of the interior of the registeringmechanism; the cover-and dials being re'mo'vedz'" q i Fig. '10 is avertical section of the same looking in the direction of thearrow'inFig. 9.

Fig. ll'i's'a diagrammaticyiew showing anoth-t erform ofmy'invention'containing two modificat io ns from"th foini shown in theother figures. \Fig. 1amadiagramshowmg the derivation of the tormula forcomputing the "radius of curvet 1 f 1 l Fig. 13 is a detail o t thelocking mechanism for settin tn'e dials."

Fig. 14 is three views of a small locking plate used in the device.

Fig. 15 is a perspective view of half of the limit cage for the centerball.

Fig. 16 is a side elevation, partly in section, showing in more detailthe form of the invention illustrated diagrammatically in Fig. 11.

Fig. 17 is a corresponding View showing still another form ofconstructing the general form of the invention shown in Fig. 11,

My apparatus consists essentially of a plurality of touching balls I, 2and 3 arranged in line. Said balls are preferably very accurately groundto known diameters (preferably all three are equal) and are mounted in aframe 4 with limited play. For simplicity in working with the instrumentit is desirable that either the radius or diameter of each of the ballshas the value unity. Preferably the end balls I and 3 are fixed againstup and down movement, each being mounted in a cage 5 and 6 respectivelyformed in the ends of the housing 4 by end blocks I and 8 and bywedge-shaped bottom pieces 9, I0 and 9, I0 which rest against the bottomside portions of each ball and prevent the same from droppingdownwardly, each ball resting at its top against a boss I I! I. Themember 4 is secured to the main frame work I2 by two pairs of machinescrews I3, I3 and I4, I4 which project through apertures in the bottomof the frame I2 and are held in place by nuts I5 and I5. Ball I may haveno lateral movement but ball 3 is provided with a limited lateralmovement being yieldingly pressedagainst the inter-' mediate ball 2 bythe spring pressed end block 8 pivoted on rod I1 and having the toe I6thereof yieldingly held against the ball by compression springs I8, I8.The middle ball 2 is mounted in an open cage I9 for limited up and downmovement. The cage is shown as comprising a pair of U-shaped pieces I9,each having thereon laterally extending threaded pins 20. The cage maybe locked in any one of a plurality of positions by inserting said pinsthrough any pair of a plurality of pairs of apertures 2|, 22 and 23 oneach side of the cage, nuts 20' being used to lock them in position. Thecage may, therefore, be placed at three different heights so as toincrease the range of possible movement of the central ball for convex,concave, or nearly fiat surfaces.

According to the preferred form of my invention, the radius of curvatureis measured by measuring the difference in elevation of the middle ballas compared to the two end balls, that is, the distance marked h inFigs. 7, 8 and 12. This distance may be considered either plus or minusaccording to whether a convex or concave surface is being measured. Aconvenient method of accurately measuring the height of the middle ballis to mount within the frame I2 an accurate micrometer gauge 25. Asshown said gauge comprises a box portion 26 containing the multiplyinggearing for actuating the main or micrometer index 21 and the coarseindex or revolution counter 28 in accordance with the position of themovable rod 29. Said rod has a foot 30 thereon which rests on top of themiddle ball 2 and is yieldingly pressed downwardly thereon by a spring3| anchored to the casing and at the upper end to a small pin 32extending laterally from said rod. Rack teeth 33 are cut on the rodwhich mesh with a piston 24 which is the first of a series ofmultiplying gears 35 which finally actuate small pinion 36 on the shaftof the index 21. A larger gear 36 meshes therewith onthe shaft 28' onwhich pointer 28 is mounted' A light coil spring 3| is also secured tosaid shaft so as to take up any back lash that may be present in thetrain of gearing.

The main dial 25' of the instrument is adjustably mounted thereon sothat it may be set in any desired position to read zero with respect tothe index 21, the dial being graduated both clockwise andcounter-clockwise for plus and minus measurements. The dial may belocked in place by a clamp 31 which is tightened and loosened at will bymeans of a set screw 38 having a knurled head 39, the clamp bearing atits upper end 40 against the knurled periphery 4| of the dial face (seeFig. 13).

The entire indicator box 26 is adjustably clamped to the spider arms 43of the framework I2. The spider arms meet at their center to form a.central hub 46, having a vertical slot 49 therein shown with enlargedends.

Slidably mounted in said slot 49 is a block 50 secured to the back ofthe indicator 26. Said block is vertically adjustable in said slot bymeans of set screws 5I5I threaded through the ends of the central hub46. By this means the gauge may be accurately positioned in theframework I2. To look it in. position there is provided a small I-shapedplate 52 which is clamped in place on the block by set screws 53. Saidplate 52 has a central aperture 54 through which projects a threadedstem 55 on the block 50. Said plate overlies at each end the centralblock or hub 46 and its middle portion is cut away to receive a lockingplate 56 (Fig. 14). Said plate also has a central aperture through whichthe stem 55 projects. It will readily be seen, therefore, that byscrewing down on the thumb nut 51 threaded on the stem 55 that the partswill be rigidly clamped in place after the height of the instrument isproperly adjusted.

Reference is now had to Fig. 12 which shows the derivation of theformula for computing the radius of curvature of a surface in terms ofeither the height h of the middle ball or the distance x between theout-er surface of the outer balls when the five points of contact madeby the balls with each other and the work surface and the three centersof the balls are coplanar.

Considering first the right triangle COP, one may write the equation:

where R is the desired radius of curvature, a, the radius of each of theballs, h is the perpendicular distance from the center of the middleball to the line joining the centers of the two outer balls, and :L' isthe distance between the outer faces of the two outer balls along a linejoining their centers.

But considering now the right triangle OO'P, one may write:

Substituting this value for Or in terms of diameters instead of radiiwhere the case of a concave surface.

D equals the diameter of the spherebeing meas- .1 .11e and i h diameterI a i -ifi bell 9? a own? s fa i el i n uces to +h i h.

' If at is chosen as unity then these equations m be'writtgn:

for concave surfaces." r

It is, of course, obvious that-if desiredthe dial maybe'gra'duatedto're'ad directly the radius of curvature being measured although inthis caseth-e graduations would not be uniform.

It will be noted that huhas beentaken a's positive in the directionupward from'the. line joining "the centers of the two-outer balls inFig. 12 and Has positive when the center of curvature lies below thethree" points of contact. This necessitates a negative value for h andimplies the negative sign for D in Equations (5) and (5') for Theinvention provides a meansfor attaining the coplanarcase In this"forwhich' (5) is derived by simply rocking the instrument in a planeperpendicular to the line 'joiningthe'centers'of the two outer ballsuntil a maximum h is noted. a

Fig; :11 shows a simple method of measuring the lateral displacementofthe outside balls instead ofthe up and down movement of the middle ball.fase a: in the above' equations is being meas'iiredinstead of Theworking equation of the instrument for thiscasefanbe similarly derivedfrom '(1) and 1(2) by the elimination of h. 5

j It is clear that any combination of three balls having difleringradiican be used, the combination desired dep-ending upon the particularproblem in hand. A particular c'aseis one in which the middle ball has aradius a, which is smaller than the radius a of the] two outer balls(Figsll).

The advantage o f this arrangement lies in the tendency.totholdthemiddleball against-"the work rather thanto' push it awayfrom'the work as is the case under certain circumstances with threeequal balls. In this case Equation (4) becomes It is to be noted that inthe case of the three equal balls, the h in Figs. '7 and 8 is equal to hin Equations (4) and (5). However, in case the middle ball has a radiusa a the measurable quantity, namely the rise of the top surface of themiddle ball above a line across the tops of the outer balls, is notequal to h of Equation (6) but h where bearing in mind the conventionthat h is positive when the displacement is above the line across thetops of the two outer balls. I

In the apparatus according to Figs. 11 and 1 the outside balls are againmarked l and 3 and the middle ball 2'. The distance as is shown asmeasured by a pair of parallel jaws Bil-Bl, the former being fixed to agraduated bar BZ and the at e. th eade thescrew 63 i malle in the hair.Itwinr a 'flv ejseen t at ,b'ylt rn ns the .knurled had BA'flthejaw'lfi'l may be movedagainst jheib'all sso as'to measure the distancewon the scale .'65and the micrometer scale 66 on the aar:.63..jllhejtlire balls; as before, maybe supported in a cage 6110f whichthe fixed jaw to may form one end, the movable jaw .being" slida'bly"mounted.between the side walls of the cage." ,flhe centerlbiall .2"isshown ias yieldin'gly pressed downwardly into engagement with theworklby means .said spring and plungerbeing supporteddn'fa fbraclget 10secured to theft'op of the framework 1 I which supports the cage. Ahandle 66' may loe provided'iorpressing theball into engagement i ihwork- Theren of measuring gauge shown in Figs. ,1 and 2 may also beemployed'for measuring the lateralsepafation of the balls. Such aconstrue tipn is shown in Fig.'.1.7,in which the ball are supportedin'a'cage 4" and thelateral movement of the end ball 3 is measured" by agauge. mounted in aframewqrk [2" secured to thecafge at one end. Thegauge 25may be in all respects the sameas the gauge in Fig. Lexcept thatitis placed horizontal and read from the top. Assuming the gauge of Fig..1 tobe correctly ,mquhted inthe frame l2, the apparatus .is used bygrasping Tthe ha ndle 56 in the hand and press'ingthje balls downagainst the surface tdbe measured. The gauge I9 is adjusted'inthe proper.holes so as not to fint'erferewlth the vertical movements of therniddleball 2. The handleis then forth in order 'that the op- ;e ator may mal esure thatfthe Icorrect reading isobtained an thegauge is read when'them'axdmum curvature is shown.

a In accordance with the provisions of the patent statutes, I haveiherein described the principle and operation of my invention, togetherwith the apparatus whichI now consider. to'jrepresent the .beste'mbodiment thereof, but I desire" to have'it .lliidQt iQ d th he.ap rai Shown i 'Q y illustrativeaiid thatlthe invention can be carried 01it". ]o y other means. "Also, while it is designed touse thelvariousfeatures and elementsin the IQornbinatiOIirand relations described, someof thesemaybe 'altered and others omitted without interfering with the[more general results "butlined, and the invention extends to such use.

fla lin dsqrib s m i en iq Wha Claim and desire to su're by LettersPatent is:

1. A spherometer comprising a plurality of touching balls, means formounting the same to permit lateral separation of the outer balls and upand down movement of a middle ball so that 7 all balls may rest on thework, and micrometer permit lateral separation of the outer balls and Iup and down movement of a middle ball so that all balls may rest on thework, and micrometer means for measuring the lateral movements of saidouterballs.

4. A spherometer comprising a cage or housing for adjustably supportingthree balls in a row for conforming engagement with the work, yieldingmeans for pressing the outer balls against the middle ball, yieldingmeans for pressing the middle ball downwardly against the work, and agauge for measuring the up and down movement of the middle ball.

5. A spherometer comprising a cage or housing 'for adjustably supportingthree balls in a row, yielding means for pressing the outer ballsagainst the middle ball, a vertical rod engaging the top of the middleball, resilient means holding said 'rod against said ball, and amicrometer means :for indicating the vertical movements of said rod.

6. A spherometer comprising three balls adapted to be brought intocontact with the measured surface and having five points of contact withthe work and with one another lying in the same plane, means forsupporting the end balls for limited lateral movement and the middleball for vertical movement and means for measuring the variations invertical movement of the center ball with respect to the other two.

7. A spherometer comprising a cage or housing for adjustably supportingthree balls of equal diameter in a row for conforming engagement withthe work, yielding means for pressing the .outer balls against themiddle ball, yielding means for pressing the middle ball downwardlyagainst the work, and a gauge for measuring the up and down movement ofthe middle ball.

8. A spherometer comprising three balls adapted to be brought intocontact with the measured surface and having five points of contact withthe work and with one another lying in the same plane, means forsupporting the end balls for limited lateral movement and the middleball for vertical movement the middle ball being smaller than the othertwo, and means for measuring the variations in vertical movement of thecenter ball with respect to the other two.

9. A spherometer comprising a cage or housing for adjustably supportingthree balls in a row, yielding means for pressing the outer-ballsagainst the middle ball, a vertical rod engaging the top of the middleball, resilient means holding said rod against said ball, a micrometergauge for measuring the movements of said rod, a frame secured to saidcage, and means for adjustably mounting said gauge in said frame.

10. A spherometer comprising a cage or housing for adjustably supportingthree balls in a. row, yielding means for pressing the outer ballsagainst the middle ball, a vertical rod engaging the top of the middleball, resilient means holding said rod against said ball, a micrometergauge for measuring the movements of said rod, a frame secured to saidcage, means for adjustably mounting said gauge in said frame, and meanswhereby the zero point on the gauge may be adjusted.

11. A spherometer comprising three balls adapted to be brought intocontact with the measured surface and having five points of contact withthe work and with one another lying in the same plane, a cage forsupporting the end balls for limited lateral movement and the middleballfor vertical movement, means for yieldingly pressing said middle ball inengagement with the measured surface and means for measuring thevariations in lateral position or spacing of the outer balls.

12. A spherometer comprising a plurality of linearly arranged touchingballs of equal diameter adapted to rest on the work, a cage for fixedlysupporting one end ball and the other end ball for limited lateralmovement only and a middle ball for vertical movement and means formeasuring relative up and down movement of a middle ball with respect tothe other balls for measuring the radius of curvature of the work interms of the diameter of the said balls.

13. A spherometer comprising a plurality of touching balls of equaldiameter adapted to rest on the work, a cage for fixedly supporting oneend ball and the other end ball for limited lateral movement only and amiddle ball for vertical movement, means for yieldingly pressing themiddle ball against the measured surface and means for measuring lateralseparation of the outer balls for measuring the radius of curvature ofthe work in terms of the diameter of the said balls.

14. A spherometer comprising a pair of outer balls of equal diameter, amiddle ball of lesser diameter, a cage for supporting the end balls forlimited lateral movement and the middle ball for vertical movement allof said balls being adapted to rest on the work and to touch theadjacent ball, and means for measuring relative movement of said ballsfor measuring the radius of curvature of the work in terms of thediameters of the said balls.

HORACE H. WILLIS.

